Hello,
You shouldn't have any problems in principle. I've had success compiling Qt (at least the core modules) with the intel compiler on the cluster in the university. It is supported, which is upheld by the fact of having a mkspec for icc/icpc (and bugs related to it ;)). My advice is to first compile the Qt modules you'd need for your application with the intel compiler. If you meet no problems, then your porting should be smooth sailing.

Kind regards.

PS:
Most probably the lack of popularity of the intel compiler is caused by its price ...

Even if we accept, as the basic tenet of true democracy, that one moron is equal to one genius, is it necessary to go a further step and hold that two morons are better than one genius?